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Good day students welcome to mathgotserved.com in this clip were going to be going over the second example on how to find the domain of rational functions algebraic we okay so let's take a look at the directions for the example we are to find the domain of the following rational function so for number two we have the rational function F of X equals two X times X minus three divided by X was three times two X minus three okay so indicate it in problem number one if you want to find the domain of a rational function of this nature all you have to do is find the value of X value or values of X that causes the entire expression to be undefined so what causes and expression to be undefined any value that causes the denominator to have a value of zero result in the entire expression becoming undefined okay so our focus will be or should be on the denominator so when you look in our the domain the rational function we just have to do is so for when the denominator is equal to zero and you are going to exclude the answer is from your domain okay it does values are excluded from the domain you guaranteed to have is defined outputs for all your inputs right so take a look at this example what is the denominator the denominator is the product of these two quantities X was three times two X minus three okay so said it equal to zero and then we'll solve this graphic equation one assault is that the quadratic equation our answer is shift be excluded from the domain and will have the domain on this function right so how do we so the quadratic equation in fact other for to solve this one apply the zero product property okay just basically says that is the product of two numbers are is zero then one of the numbers have to be zero okay so you X was three is equal to zero or two X minus three is equal to zero are isolate going to have two values to be excluded from the domain of this function right here let's all the first one subtract three from both sides X equals negative three and then take a look at the second equation all you do is you look at three to both sides in divide by two okay so is go ahead and do this as three to both sides that yields two X equals positive three and then divide both sides by two that will isolate express and then we'll have X equals three over to write so the question is what these two values mean what is this me well these two values when you plug it into this function you will have on defined outputs so that means those numbers have to be excluded from the domain right so how do we write our final answer is going to write down the domain is the set of X is such that X cannot the negative three and X cannot be three over to okay and any other value you and eight defined outputs for this function so the domain restricts X is so everything apart from these values right here so X cannot be the/there X cannot be negative three and X cannot be three over to so that's the domain of our function right so that's that the thanks so much for taking the time to watch this presentation really appreciated the free to subscribe for channel for updates to other cool tutorials such as this you have any questions or like to request's tutorials for us to make for you feel free to included in the comments section below this video more clips can be, mathgotserved.com exiting for watching and have a wonderful day